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VirtualBox is complaining that the kernel module is not loaded. Please
run `VBoxManage --version` or open the VirtualBox GUI to see the error
message which should contain instructions on how to fix this error.

指示通りにrootで

VBoxManage --version

を実行。
すると、以下のようなメッセージが出現した。

WARNING: The vboxdrv kernel module is not loaded. Either there is no module
available for the current kernel (3.10.0-514.el7.x86_64) or it failed to
load. Please recompile the kernel module and install it by
sudo /sbin/vboxconfig
You will not be able to start VMs until this problem is fixed.
5.1.22r115126

This system is not currently set up to build kernel modules (system extensions).
Running the following commands should set the system up correctly:
yum install kernel-devel-3.10.0-514.el7.x86_64
(The last command may fail if your system is not fully updated.)
yum install kernel-devel
vboxdrv.sh: failed: Look at /var/log/vbox-install.log to find out what went wrong.
This system is not currently set up to build kernel modules (system extensions).
Running the following commands should set the system up correctly:
yum install kernel-devel-3.10.0-514.el7.x86_64
(The last command may fail if your system is not fully updated.)
yum install kernel-devel
There were problems setting up VirtualBox. To re-start the set-up process, run
/sbin/vboxconfig
as root.

No usable default provider could be found for your system.
Vagrant relies on interactions with 3rd party systems, known as
"providers", to provide Vagrant with resources to run development
environments. Examples are VirtualBox, VMware, Hyper-V.
The easiest solution to this message is to install VirtualBox, which
is available for free on all major platforms.
If you believe you already have a provider available, make sure it
is properly installed and configured. You can see more details about
why a particular provider isn't working by forcing usage with
`vagrant up --provider=PROVIDER`, which should give you a more specific
error message for that particular provider.